Spatial modulation (SM) uses antenna indices to transmit information, along with modulation symbols. The conventional SM scheme fixes the number of active antennas, and consequently the number of transmit symbols, in a transmit vector to avoid detection ambiguity. This work proposes a generalized block-based spatial modulation (GBSM) scheme which varies the number of active antennas in each transmit vector, but fixes their number over a transmission block. The proposed GBSM scheme, which transmits information using the spatial dimensions created over a block of transmit vector, resolves detection ambiguity as the number of transmit symbols over a block remains fixed. It crucially also has a large constellation cardinality, which we exploit by proposing novel low bit error rate (BER) constellation design algorithms. We also propose a novel low-complexity semi-definite relaxation detector, which has similar BER as that of the optimal maximum likelihood detector but with ≈ 85% lower complexity.